Jamming Percolation in Three Dimensions

Abstract

We introduce a three-dimensional model for jamming and glasses, and prove that the fraction of frozen particles is discontinuous at the directed-percolation critical density. In agreement with the accepted scenario for jamming- and glass-transitions, this is a mixed-order transition; the discontinuity is accompanied by diverging length- and time-scales. Because one-dimensional directed-percolation paths comprise the backbone of frozen particles, the unfrozen rattlers may use the third dimension to travel between their cages. Thus the dynamics are diffusive on long-times even above the critical density for jamming.

6 pages, 6 figures

References in corpus (9)

• Glassy dynamics of kinetically constrained models
• The Jamming Transition in Granular Systems
• Geometric Frustration in Buckled Colloidal Monolayers
• Spiral Model: a cellular automaton with a discontinuous glass transition
• Direct measurements of the dynamical correlation length indicate its divergence at an athermal glass transition
• On the study of jamming percolation
• Spiral model, jamming percolation and glass-jamming transitions
• Jamming transition of kinetically-constrained models in rectangular systems
• Jamming by Shape in Kinetically-Constrained Models

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• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Hydrodynamics in kinetically-constrained lattice-gas models
• The relation between the structure of blocked clusters and the relaxation dynamics in kinetically-constrained models
• Jamming vs. Caging in Three Dimensional Jamming Percolation
• Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models
• The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model
• Percolation in Networks of Liquid Diodes
• Kinetically constrained model for gravity-driven granular flow and clogging
• Constraint relaxation leads to jamming